Which linear algebra book should I read to understand vectorized operations?
If you already have two years of a bachelor's of mathematics, I recommend part I of the book that you're mentioning. That part of the book reviews the main mathematics used in the optimization of neural nets (in part 1), and then actually goes through the various models in detail in the later parts. The review is done at a level that is suitable for someone who has already studied these topics, but needs a refresher.
The book Matrix Differential Calculus with Applications in Statistics and Econometrics covers more advanced topics, which might also be what you are looking for. There is also the related Wikipedia article.